Oscillating-Field Current-Drive Experiment on MST K. J. McCollam, J. K. Anderson, D. J. Den Hartog, F. Ebrahimi, J. A. Reusch, J. S. Sarff, H. D. Stephens, D. R. Stone University of Wisconsin-Madison D. L. Brower, W. X. Ding University of California, Los Angeles 52nd Annual Meeting of the APS Division of Plasma Physics 8-12 November 21 Chicago, Illinois
Oscillating-field current drive (OFCD) is a proposed method of efficient, steady-state current drive in which applied AC poloidal and toroidal loop voltages interact with magnetic relaxation to produce a DC plasma current. OFCD at a moderate power level is added to Ohmically sustained reversed-field pinch plasmas in the MST device, and its effects on equilibrium profile evolution, global magnetic fluctuations, and energy balance are examined using a variety of measurements. For the optimal phase between the two applied AC voltages, the cycle-average plasma current increases by up to 1% with Ohmic efficiency, while both the energy confinement time τ E and normalized thermal pressure β slightly improve, consistent with a reduction in magnetic fluctuation amplitudes. Nonlinear, 3D, resistive-mhd simulations reproduce the main experimental features, especially the phase dependence of the added current. Internal fluctuation measurements are underway to examine changes in the relaxation dynamics. A new programmable power supply is to be used in optimizing OFCD performance with longer pulses, more power, and improved waveform control, including nonsinusoidal OFCD.
Efficient Current Drive with Good Confinement an RFP Goal Oscillating-field current drive (OFCD), which uses poloidal and toroidal AC loop voltages phased to inject DC magnetic helicity, is the chief candidate for efficient, steady-state sustainment of the reversed-field pinch (RFP). Global OFCD current drive relies on induced magnetic relaxation which could affect energy confinement. In Madison Symmetric Torus (MST) experiments OFCD efficiently increases plasma current by up to about 1% while reducing edge-resonant magnetic fluctuations and slightly improving energy confinement. In experiments the OFCD phase of maximum added current is not the phase of maximum helicity-injection rate, a result reproduced by nonlinear, resistive-mhd simulations of the experiments.
Outline RFPs OFCD MST Experiments and MHD Simulations New Power Supply and Future Work Conclusion
RFPs
RFP Can Have High Beta ( p/b 2 ) Highly sheared magnetic field mostly due to plasma current Present RFPs sustained by transient toroidal induction Bootstrap current is small
Magnetic Tearing Modes Resonant in RFP Resonant surfaces for (m, n) modes where safety factor q = rb φ R B θ = m n m = 1 modes resonant in core q.2.1 Safety Factor vs. Radius 1/6 q resonant 1/71/8 = m/n m=1... m= /n m = modes resonant in edge at reversal surface -.1.2.4.6.8 1 r/a
Magnetic Relaxation Governs Standard RFP B m,n [G] V loop [V] B [G] 2 15 1 5-5 5-5 -1 3 2 1 RFP Signals vs. Time B (a) <B > B (a) V V B,n (a) B 1,n (a) 2 25 3 t [ms] B [G] a q 4 3 2 1 5 4 3 Equilbrium Model Profiles vs. Radius B (r) B (r) 2 1 [1-(r/a) ].25.2.15.1.5. -.5 -.1.2.4.6.8 1 r/a Quasiperiodic sawtooth magnetic relaxation events tend to maintain flat λ J /B profile by fluctuation-induced EMF despite peaking tendency from toroidal induction Relaxation can be transiently suppressed with inductive current-profile control
Oscillating-Field Current Drive (AC Helicity Injection or F-Θ Pumping)
DC Sustainment by Applying AC Loop Voltages Poloidal and toroidal: V θ sin (ωt) & V φ sin (ωt δ) Magnetic helicity: K A Bdv ΨΦ ( Iφ 2 in RFP) Helicity balance: K =2V φ Φ 2 ηj Bdv (injection minus decay) Vˆ sin( ) Vˆ sin( - ) Time-average OFCD helicity injection rate: K inj = V θ V φ /ω sin δ (maximum at δ = π/2)
Magnetic Relaxation Required for Global Current Drive OFCD generates EMF at edge via axisymmetric oscillations: E = V B 4 3 DEBS MHD Code EMF from Oscillations 2 Edge-driven current drives magnetic fluctuations B EMF 1 EMF from Fluctuations Nonaxisymmetric fluctuations generate EMF throughout plasma including core: E = V B -1..2.4.6.8 1. r/a Radial direction of current transport is opposite to that in standard RFP
Full Sustainment Modeled in 3D Nonlinear Resistive MHD Large equilibrium modulation required Magnetic-fluctuation level similar to that for standard RFP I 4 3 2 DEBS MHD Code (S=5x1^5) OFCD cycle-averaged Standard RFP 1 Confinement at high Lundquist number S τ R /τ A unknown..5.1 t/ R.15.2
Required Modulation for Full Sustainment Smaller at Higher S Modulation required at MST s S is above the standard range Required OFCD Modulation in Relaxed-State Power Balance Standard Range Experimental drawbacks of large modulation: Hardware requirements MHD fluctuation activity due to equilibrium changes q(a).5 1. MST Reactor 1.5 1 4 1 6 1 8 1 1 S= / R A Periodically low plasma currents
MST Experiments and MHD Simulations
Madison Symmetric Torus (MST) R /a = 1.5 m/.52 m I φ 6 ka T e,i 2kV n e 1 19 /m 3 Al shell 5 cm thick
1% Plasma Current Added in MST Drive or anti-drive chosen by phase δ Current-drive efficiency is Ohmic ( I φ 2 ka, P 2 kw) ka 3 2 1 Plasma Current vs. Time Drive Off Anti-CD Added current I φ limited by τ pulse < L/R 1 2 3 4 ms 5 6 7
OFCD Modifies Equlibrium Profiles and Magnetic Fluctuations V [V] V [V] B m= [G] 15-1 2-2 1 15 OFCD OFF 2 22 24 26 28 t [ms] OFCD ON ( = /8) OFCD ON ( = /2) 22 24 26 28 22 24 26 28 3 t [ms] t [ms] Toroidal Loop Voltage Poloidal Loop Voltage Flat Peaked Magnetic Fluctuations RFP sawtooth relaxation cycle entrained to OFCD cycle For δ = π/8, current profile more quiescent and m = decreased For δ = π/2, current profile less quiescent and m = increased
Added Current Maximum at δ π/8 DEBS nonlinear resistive-mhd code simulations agree with experiments Helicity decay rate ηj Bdv maximum at δ π/2 m = fluctuations minimized and confinement maximized at δ π/8 ka Wb2/s Wb2/s G ms 2-6.5-1. 2.6 1.4 8 1.6.4 OFCD Phase Dependences Added Current Total Helicity Decay Rate Experiment OFCD On: Experiment OFCD Off: MHD Code OFCD On: OFCD Helicity Injection Rate Edge-Resonant B Fluctuations Energy Confinement Time -.5..5 1.
Optimum OFCD Induces Large Thermal Pressure Oscillations Cycle-average energy confinement time τ E and beta (β p/b 2 ) slightly improved in OFCD at δ = π/4 Pressure oscillation mainly due to cyclic mechanical heating rather than Ohmic heating n e T e [1 19 3 ] 3 2 1 Electron Pressure vs. Radius ( ) On Average Off Average..2.6.8 1.
Both Oscillations and Fluctuations Affect Pressure Evolution For δ = π/2 there is a periodic pressure drop when m = magnetic fluctuation amplitude becomes large For δ = π/4 fluctuations are lower and pressure oscillation mainly follows mechanical heating rate w th = (5/2)p V (3/2)V p due to applied oscillations r/a r/a r/a r/a 1.. 1.. 1.. 1. Thermal Pressure Contours (color) & Magnetic Flux Contours (lines) plasma current trace reversal surface m= magnetic fluctuation trace p (J/m^3) 1 8 6 4 2 magnetic flux:. 21 22 23 24 t (ms)
Fluctuations Induced by Oscillations Depending on Phase For δ = π/2: Parallel drive E B large when radial flow E B is outward λ profile becomes flatter as m = amplitude increases This activity is reduced for δ = π/4 with otherwise same OFCD settings B [G] B [G] 1. 1. Magnetic Fluctuations ExB: ExB: E B: Magnetic Fluctuations E B: t [ms]
MHD Activity Seems to Limit Added Current at Higher Power Contributing factors: Large oscillating electric field E ka 4 2 Two Individual Pulses vs. Time Added Plasma Current Wall conditions Programmable power supplies for OFCD might help: Lower frequency to lower E Nonsinusoidal waveforms G -2 2 15 1 5 m= Magnetic Fluctuations 15 2 25 3 35 4 t [ms]
New Power Supply and Future Work
Present Power Supplies Are Two Tank (LC) Circuits Switched by novel ignitron method OFCD PFN start Precharged for immediate full amplitude MST PFN Tank Circuit MST I' -I' Powered by pulse-forming network (PFN) Feedback Circuit
New Programmable V θ Power Supply on MST Improved waveform control for more OFCD flexibility with higher input power Bm= [G] 4 3 2 MST 119851, 52, 56, 57 Edge-Resonant Magnetic Fluctuations 1 Initial tests of nonsinusoidal OFCD to study and perhaps control MHD activity B (a) [G] -1-2 -3 Edge B Adding programmable V φ later could enable longer MST pulses with more OFCD current and better characterization of current drive E (a) [V/m] -4-5 1 5-5 -1 25 3 35 t [ms] Edge E
Future Work Use programmable power supplies to maximize added current Flexible waveforms, longer pulselengths, higher power Feedback to constant I φ to avoid L/R time limit Experimental Topics MHD activity and magnetic relaxation Ion heating and confinement Plasma-wall interactions Numerical MHD computation to model MST experiments Explore parameters, include transport effects
Conclusion
Summary OFCD might allow efficient, steady-state full RFP sustainment, but its reliance on magnetic relaxation motivates further study of its confinement properties. In MST experiments OFCD efficiently increases plasma current by up to about 1% while reducing edge-resonant magnetic fluctuations and slightly improving energy confinement. In experiments the OFCD phase of maximum added current (δ π/8) is not the phase of maximum helicity-injection rate (δ = π/2), a result reproduced by nonlinear, resistive-mhd simulations of the experiments using the DEBS code. Future plans call for experiments using programmable power to maximize added current and focused on MHD activity, magnetic relaxation, and energy confinement, with the aid of continuing MHD simulation.
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